Spectral methods: some applications in physics

Abstract

Spectral methods are powerful tools in natural sciences and in various areas of engineering, the purpose of this work is to show how to apply spectral methods to three physics problems, solution of the diffusion equation, calculation of the third coefficient of the virial and its first and second derivatives for the modified Lennard-Jones potential of a simple fluid and periodicity detection of a mechanical system. The approach is computational, considering that the required Fourier transforms, sine and cosine Fourier transform can be easily implemented in their fast version in any programming language.